An Enhanced Study of the Load–Displacement Relationships for Rolling Element Bearings

An enhanced analytical approach is suggested for calculating three rolling element bearing loads F_x, F_y, and F_z as well as the two tilting moments M_y and M_z as a function of five relative race displacements: three translations dx, dy, and dz, and two tilting angles dθ_y and dθ_z. A full coupling between all these displacements and forces is considered. This approach is particularly recommended for programming the rolling element bearing behavior in any finite element analysis or multibody system dynamic tool, since only two nodes are considered: one for the inner race center, usually connected to a shaft, and another node for the outer race center, connected to the housing. Also, roller and raceway crown radii are considered, meaning that Hertzian point contacts stiffness can be used at low load with a smooth transition toward Hertzian line contact as the load increases. This approach can be used for describing any rolling element bearing type when neglecting centrifugal and gyroscopic effects and applying the approximation of a constant ball–race contact angle. Deep groove ball bearings (whose contact angle sign follows the sign of the applied bearing axial force) or other ball bearings or spherical roller bearing operating under large misalignment may not support such approximations.